Residue-guided phase unwrapping in fringe projection measurements using second differences

This paper presents an innovative algorithm for unwrapping 2D phase maps with discontinuities. The method employs residue detection for identifying affected areas at a coarse scale. Unlike traditional techniques relying on subjective assessment, this algorithm automates threshold determination, ensuring precision without manual intervention. At the pixel level, it utilizes a bitmap mask based on second differences and the geometric mean formula to locate inconsistencies within the wrapped map precisely. This coarse-to-fine process establishes an optimal threshold for the second difference mask, resulting in highly accurate unwrapped outcomes while maintaining computational efficiency. Compared to conventional methods, this approach delivers superior unwrapped results, making it suitable for diverse applications. Experimental validation includes computer-simulated surfaces and practical fringe projection systems, accompanied by a thorough error analysis.